Lagrangian Data example for PDE-FIND

[scottmayberry]

Is your feature request related to a problem? Please describe.

I do not see a lagrangian data example in the PDE-FIND documentation, although it is mentioned it is possible in Rudy et al (see Figure 2). In the paper, the authors sample the movement of a random walker to reproduce the diffusion equation. My problem involves multiple robots traveling in an unknown PDE field, taking measurements. My goal is to use the data collected to reconstruct the PDE, but I cannot find an example similar in the documentation.

Describe the solution you'd like

An example not using the spatial grid in PDE-FIND, instead using the trajectory of a particle/robot in a PDE field would be very much appreciated. Or pointing me towards a source that has an example (or further readings).

Describe alternatives you've considered

I've tried interpolating spatial data from the trajectories to create a spatial grid, but the interpolation is too noisy.

Additional context

Rudy, S. H., Brunton, S. L., Proctor, J. L., & Kutz, J. N. (2017). Data-driven discovery of partial differential equations. Science Advances, 3(4). https://doi.org/10.1126/sciadv.1602614

[scottmayberry]

I figured out how to do it, and Ill try to upload my example here in the future for consideration.

[Jacob-Stevens-Haas]

This would be very cool, and something frequently requested of pysindy by the financial math community. Agree that the Rudy paper mentions that it's possible, even if it's not clear how they did it. I'm not sure how the current codebase would be able to accomplish that, however, so if you've been able to accomplish it, I'd be excited to see how.